"Central bank LSAPs potentially may affect interest rates through at least three channels. Notably, all three channels can broadly affect longer-term interest rates, extending beyond those securities that the central bank announces it will purchase:

A portfolio balance channel, because the supply of long-maturity bonds available to private investors is reduced. The reduced supply of longer-term securities targeted by the Fed lowers the amount of interest rate risk in investor portfolios. That in turn decreases the risk premium that they require to hold both the targeted securities and other assets of similar duration. Longer-term interest rates are lowered across the board as a result. Gagnon et al (2011) emphasize this channel for QE1.

A signaling channel, which arises when the Fed's announcements are interpreted as signals of its intent to hold down short-term interest rates further into the future. Bauer and Rudebusch (2011) argue that this channel played an important role for QE1.

A market functioning channel, because QE1 provided relief when conditions in financial markets were dire, liquidity very low, and panic widespread. The Fed's intervention calmed investor fears. Thus, the intervention substantially supported a range of asset prices, including MBS and corporate bonds, lowering their yields."

"We use empirical pricing models for MBS yields in the secondary mortgage market and for mortgage rates paid by homeowners in the primary mortgage market to measure how distorted mortgage markets were prior to the Federal Reserve's intervention, and the course of market risk premiums during the restoration to normal market functioning...

"We argue that this return to normal pricing occurred because the Federal Reserve's announcement signaled a strong and credible government backing for mortgage markets in particular and for the financial system more generally...

"More specifically, we estimate that the Federal Reserve's MBS purchase program over the course of 16 months reestablished normal market pricing in the MBS market and resulted in lower mortgage rates of roughly 100 to 150 basis points for purchasing houses. Most of the decline in mortgage rates occurred between the announcement of the program, on November 25, 2008, and the implementation of the program in the first quarter of 2009. After this point, both mortgage rates and risk premiums remained relatively stable until the end of the Federal Reserve MBS purchase program."

Hancock and Passmore note that the portfolio balance channel may have played a role after the completion of the QE1 purchases once market functioning had normalized, but the biggest bang was that renormalization itself.

Bauer's observations align with Hancock and Passmore's conclusions:

"QE1 had very pronounced effects on interest rates. The key announcements led to decreases of close to one percentage point. The announcements not only lowered yields on targeted Treasury securities and MBS, but also on corporate bonds...

"The two other programs, QE2 and MEP [maturity extension program], also affected yields of securities that were not targeted for Fed purchases... Generally though, QE2 and MEP affected interest rates much less than QE1 did. One reason is that bond market functioning had largely returned to normal. In addition, expectations of future short-term interest rates were already very low when these programs were announced, leaving little room for further signaling effects. Finally, QE2 and MEP were smaller than QE1."

Earlier this week, in a speech delivered in Tokyo at the Institute of Regulation and Risk, Federal Reserve Bank of Atlanta President Dennis Lockhart provided his view on this evidence:

"In my view, these [the QE1] purchase programs played an important role in the transition away from the emergency lending facilities created earlier in the crisis. The emergency credit facilities worked well to stem the downward spiral of the immediate post-Lehman period. Financial markets began the process of repair during the first half of 2009 but were still suffering from relatively serious liquidity pressures. The QE1 operation sustained the liquidity support that had been previously provided by lending through the emergency facilities.

"Because asset purchases largely replaced emergency loans made during the crisis, the net increase in the Fed's balance sheet was relatively modest. In this sense, the quantitative easing label is misleading. The intent and effect of the policy was not to inject a new and sizable quantity of reserves into the economy. Rather, the effect was to sustain liquidity in still struggling and fragile financial markets, particularly those related to residential real estate. For that reason, I prefer the term ‘credit easing' to describe this policy action."

However, the smaller impact of QE2 leads Lockhart to a different conclusion regarding the largest contribution of that program:

"I view QE2 differently. The FOMC [Federal Open Market Committee] formally announced QE2 in November 2010, with its decision to purchase $600 billion in longer-term Treasury securities. However, the policy was signaled in an important speech from Federal Reserve Chairman Ben Bernanke in August of that year. The circumstances at the time were dominated by a falling trend in measured inflation, weakening inflation expectations, and rising probabilities of outright deflation. Each of these developments was effectively reversed as the expectations for QE2 took root, expectations that were ultimately validated by FOMC action.

"Unlike QE1, QE2 did materially expand the size of the Federal Reserve's balance sheet. In my view, this distinction is important. The intent and effect of the two rounds of asset purchases were different. QE1 served to maintain liquidity at a time when financial markets were exceptionally unsettled. In contrast, QE2 was a more traditional monetary action to preserve price stability."

In a sense, this places the effects of QE2 in the signaling channel category, albeit with an emphasis on inflation expectations rather than interest rates directly.

Bauer's article also covers post-QE2 policy—the maturity extension program (MEP, or "Operation Twist") and the insertion of specific calendar dates (currently at least late 2014) to provide forward guidance on the period of time that the FOMC anticipates that the federal funds rate will remain at exceptionally low levels. Lockhart also describes these policies in terms of the "signaling channel," though in these cases with interest rate effects front and center:

"In terms of intent and effect, I think of the explicit forward guidance and the MEP in similar terms. We have entered a phase of the recovery in which sustained monetary accommodation is warranted in order to preserve and advance what is still modest progress on employment and economic growth. Importantly, this modest progress is occurring in the context of what, for me, is acceptable performance with respect to our price stability mandate. Actions that reinforce the maintenance of policy accommodation are appropriate. It is through that lens that I view the MEP and explicit forward guidance on policy rates."

Lockhart's remarks provide his perspective on three somewhat distinct policy challenges—market dysfunction, disinflationary pressures, and a need to sustain monetary policy accommodation—that motivate his support for the three major policy initiatives of the postcrisis period:

"Let me summarize this brief tour of postcrisis monetary policy. I view the sequence of nontraditional monetary policy actions as tailored responses to the particular needs of the economy and financial system at the time they were implemented. My conclusion is that by and large policy actions have been appropriate to the diagnosis of circumstances at the time. And in my assessment they have worked pretty well."

In this light, President Lockhart delivers his policy punch line:

"I have reframed to some extent the original question of what more can be done around the point that policy actions must be matched to circumstances. The challenge policymakers face is judging appropriateness of a tool for circumstances. As popular as it might be in some quarters to rule out further LSAPs (QE3, as it is known), I do not think this option can be taken off the table. QE3 will work under the right circumstances. But I don't believe such circumstances prevail at this time."

By Dave Altig, executive vice president and research director at the Atlanta Fed

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"...places the effects of QE2 in the signaling channel category, albeit with an emphasis on inflation expectations rather than interest rates directly."

yep, also keep in mind:
1. if the Fed is credibly setting inflation expectations (inflation targeting) you cannot draw any conclusions about the output gap from inflation. Wages contracts are set based on expectations in the NK framework. The correct interpretation of the SF Fed letter (see below figure 2) is that for those with bargaining power, wage increases are based on expected inflation (about the mode of the non-zero wage increases).

Thus, a credible central bank targeting inflation will get it, regardless of the size of the output gap. (That's just the implication of the expectation-augmented Phillips curve)

3. "well, there is a lot of uncertainty about the output gap. " Yep: Orphanides 1999 paper actually tells you that under such uncertainty, ngdp targeting is superior and would have avoided the errors of the 1970s when we overestimated the output gap.

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